case-control studies

Case-Control Studies

Lecture 7June 20, 2005

K. Schwartzman MD

Case Control Studies

Readings

• Fletcher, chapter 10

• Walker, chapter 6 [Case-Control Studies] from Observation and Inference, 1991 [course pack]

Objectives

Students will be able to:

1. Define the term “case-control study”

2. Explain the relationship between case-controland cohort studies

3. Understand the difference between cumulative incidence and incidence density designs

Case-Control Studies - Slide 1

Objectives

4. Calculate parameters which may be validly obtained from case-control studies, namely:

a. Odds parameters: - odds of exposure in cases- odds of exposure in controls- odds ratio

b. Risk parameters: - approximation of relative risk- attributable fraction

c. Incidence rate parameters:- incidence rate ratio - attributable fraction among the exposed- attributable fraction for the population


Objectives

5. Indicate situations in which case-control studiespermit estimation of rate differences between exposure groups

6. Highlight advantages and disadvantages of case-control studies, including key biases

7. List possible sources of controls in case-control studies

8. Identify biases which may result from

different types of control selection


Case-Control Studies

Fletcher, p. 213:

“Patients who have the disease and a group ofotherwise similar people who do not have thedisease are selected. The researchers then lookbackward in time to determine the frequency ofexposure in the two groups.”

In other words, a study population is first assembledbased on a determination as to whether subjects have or have not developed an outcome of interest.

Subjects (or person-time) are then classified as to whether an exposure of interest took place. Data on other variables (e.g. potential confounders) is also obtained.

Case Control Studies - Slide 4

Walker, 1991:

“Case-control studies constitute the major advance in epidemiologic methods of our time”

Classic example:

Doll & Hill, relationship between lung cancer

and cigarette smoking (1950)


Advantages

Useful for study of conditions that are rare and/or characterized by a long latency between exposure(s) and outcomes of interest.

May be useful in evaluating the impact ofmultiple types of exposure.

Disadvantages

May be particularly vulnerable to biases arising fromselection of subjects (most often of the control group), and measurement (estimation) of exposure


In case-control studies, data about exposure status is calculated after first determining outcome status.

However, subjects may be recruited “prospectively” (concurrently), e.g.:

- All persons aged 30-50 who are diagnosed withhypertension on the island of Montreal during 2005,within 2 weeks of diagnosis.

- Controls recruited among persons of the same agewho are newly diagnosed with appendicitis inMontreal during the same time period.


Often, outcome status is already available for all subjects (“historical”) at the time of initiation, e.g.:

- During 2005, a researcher identifies all women aged 40-50 who were diagnosed with breast canceron the island of Montreal in 2004.

- In 2005, she recruits a control group among women of the same age who had negative screening mammograms in Montreal in 2004.

Case Control Studies - Slide 8

Note that the terms

“prospective” and “retrospective”

are not very usefulwith respect to case-control studies, since data about exposure status is always retrospective (by definition).


Cohort and Case-Control Studies

Every case control study corresponds to an underlying cohort study, which is (ordinarily) hypothetical.

Example (from Doll & Hill, 1950):_____________________________________________________

Women diagnosed with lung cancer vs other diseases at 20 London hospitals

Smokers Non-Smokers Total

Lung cancer cases 41 19 60No lung cancer (controls) 28 32 60Total 69 51 120_________________________________________________________

Crude odds ratio = odds of exposure in cases/odds of exposure in controls

= (a/b)/(c/d)= ad/bc = (41x32) / (19x28) = 2.5


In the corresponding cohort study,

women from the same geographic area would be recruited and classified as tosmoking status, then followed for the development vs non-development of lung cancer.



Assuming all cases of lung cancer during the period of interest were detected,

one possible 2x2 tablewould be


Lung cancer 41 19 60No lung cancer (controls) 859 981 1,840

Total 900 1000 1,900OR = 2.5

but it could also be:Smokers Non-Smokers Total

Lung cancer 41 19 60No lung cancer (controls) 70 81 151

Total 111 100 211OR = 2.5

• The cases diagnosed and included, and thecontrols sampled, relate to the exposure experience of an underlying source population.

• In each scenario, the estimated odds of cigarette smoking among cases are 2.5 times those among controls.

• In each scenario, all cases of lung cancer were included. The size of the source population

(and hence the number of non-cases) was varied.


Cumulative incidence case-control studies

Goal is to

derive estimate of relative risks (relative cumulative incidences) of outcomes amongexposed vs. unexposed

Design:

- Cases are ascertained during a definedobservation period

- Controls are persons who did not become casesduring the period of observation.

- The underlying cohort is a fixed one (not open or dynamic).


Doll and Hill, 1950

Assume that the source population was as follows:900 smokers & 1000 non smokers - followed 5 years

Then the 2x2 table would be:


Cancer + 41 19 60Cancer - 859 981 1,840

Total 900 1,000 2,000

________________________________________________


Risk of cancer in smokers: 41/900 = 0.046

Risk of cancer in non smokers: 19/1000 = 0.019Risk ratio: 0.046/0.019 = 2.4

Odds of smoking in women with cancer: 41/19 = 2.2Odds of smoking in women without cancer: 859/981 = 0.88Odds ratio = 2.5

In the corresponding case control study we take 100% of cases, butsample the controls (60/1840 or 3.3% of all potential controls - those who happened to be admitted to hospital for some other reason).

Hence the new table is:

Smokers Non smokers Total

Cancer + 100% x 41 = 41 100% x 19 = 19 60Cancer - 3.3% x 859 = 28 3.3% x 981 = 32 60

Total 69 51 120_________________________________________________________


“Risk” of cancer in smokers: 41/69 = 0.59 INVALID “Risk” of cancer in non smokers: 19/51 = 0.37 INVALID

The “risk ratio” from this 2x2 table is also invalid

Odds of smoking among cases: 41/19 = 2.2 (as before)Odds of smoking among controls: 28/32 = 0.88 (as before) Odds ratio: 2.2/0.88 = 2.5 (as before)

General Form: Cumulative incidence case-control studies

exposure + exposure -outcome + a b | total casesoutcome - c d | total controls___________ _____________ |

total exposed total unexposed | total subjects

Odds of exposure in cases = a/bOdds of exposure in controls = c/dOdds ratio = odds of exposure in cases = a/b = ad______________________ ___ __

odds of exposure in controls c/d bc

but:but:

Odds of disease among exposed = a/cOdds of disease among unexposed = b/dOdds ratio = odds of disease among exposed = a/c = ad___________________________ ___ __

odds of disease among unexposed b/d bc


Risk parameter estimation in cumulative incidence case-control studies:

Recall that relative risk = risk of disease in exposed______________________risk of disease in unexposed

From our 2x2 table, this is: a/(a+c) = a(b+d)_______ ______b/(b+d) b(a+c)

If the disease is rare,

then a<<c and b<<d among the source population

then a+c ~ c and b+d ~ d

then a(b+d) ~ ad______ __b(a+c) bc


In a case-control study, it is then possible to estimate the attributable risk (fraction) among the exposed, even if the risk for the population is unknown.

In a cohort study, the attributable risk fraction is:

Rexp - Runexp__________Rexp

= (Rexp/Runexp) - (Runexp/Runexp)_______________________Rexp/Runexp

= RR-1_____ RR

In a case-control study, this is estimated by (OR-1)/OR


Hence, from Doll and Hill (1950),

the estimated fraction of lung cancer among female smokers which is attributable to smoking is:

2.5 -1 = 0.6 or 60%______

2.5


Incidence Density Case-Control Studies

The incidence density case-control study involves the implicit comparison of the person-time experience of cases and controls with respect to the exposure(s) of interest.

The absolute quantity of person-time sampled - and hence the sampling fraction - is unknown. This is analogous to the situation with respect to persons in a cumulative incidence case-control study.


Hence the underlying (hypothetical) cohort is an open or dynamic one.

Persons considered controls at one point in time may then become cases; they can then appear twice in the 2x2 table.

For this cohort, the general form of the 2x2 table is:


exposure + exposure -outcome + a bperson-time Pe Po

Where Pe = person-time among exposed

Po = person-time among unexposed

IRe = a/Pe and IRo = b/Po

IRR = aPo____

bPe

Suppose that all cases are counted, but the controls are sampled with respect to person-time, with sampling fraction ”f” generating the incidencedensity case-control study.


Then the 2x2 table is:

exposure + exposure -outcome + a boutcome - c = fPe d = fPo

Then OR = ad = afPo = aPo___ _____ ____

bc bfPe bPe

which is equivalent to the IRR above.

Note that this formulation does not involve any assumptions about disease rarity.

It requires that the likelihood of being sampled from thesource “population” of person-time varies as a proportion of the person-time potentially “contributed” by each individual.

For example:

A potential control subject who was absent from the geographic area of interest during most of the accrual period should have less chance of being selected than a potential subject who was present throughout.

As with the cumulative incidence design, validity hinges on the assumption that f (the sampling fraction) does not vary with exposure status.


An example of an incidence density case-control study:

• A researcher wishes to evaluate the association between the use of nonsteroidal anti-inflammatory drugs (NSAIDS) and ventricular tachycardia (VT)

• In an open cohort study lasting 2 years, subjects are recruited and classified as to exposure status (NSAID use), then followed for development of VT

• In principle, it is possible to document periods of exposure and non-exposure for individuals,e.g. months on/off medication, as long as exposure is somehow reassessed


Then for the cohort, incidence rates and an incidence rate ratio can be calculated for the exposed vs unexposed person-time experience, e.g.

NSAID No NSAID Total

VT, cases 80 40 120Person-years 800 1200 2000Incidence 0.1/p-y 0.033/p-y 0.06/p-y

The estimated incidence rate ratio is:

80/800_______40/1200

= 3

So, assuming no confounding, we estimate that the incidence of ventricular tachycardia among NSAID users is 3 times that among non-users


Suppose we instead devise a case-control study.

Here, cases will be defined by a first diagnosis of VT at Montreal hospitals, and

controls will be recruited among persons who visit the eye clinics of the same hospitals:

both over a 2-year accrual period.

They will be compared with respect to use ofNSAIDS within the last 24 hours prior to presentation.

If sampling is done correctly (e.g. the probabilityof selection is unrelated to NSAID use) thenthe controls should represent the person-time experience of the source population


• If a possible control spent half the accrual period on NSAIDS, and half off, he has a 50% chance of contributing to the “exposed” group and a 50% chance of contributing to the “unexposed” group

• This individual will contribute one or the other, depending on the date of the visit chosen as control;

but in a larger group of people, the control days sampled will reflect the proportion of exposed person-time

• A person can be a control early in the accrual period and a case later

• In principle, a single person can also be sampled repeatedly as a control if the time window for exposure definition is short (more complicated in terms of analysis)


Suppose that the case-control study includes all cases which would have been detected with the open cohort design.

Two controls are recruited per case. This (unbeknownstto the researchers) corresponds to a sampling fraction for controls of 0.12 person-day sampled per person-yearof follow-up that would have occurred in the open cohort.


Then the 2x2 table is:

NSAID No NSAID Total

VT, cases 80 40 120No VT(controls) 800*0.12 1200*0.12 2000*0.12

= 96 = 144 = 240_____________________________________________

Total 176 184 360

OR = (80x144)/(40x96) = 3.0 same as earlier IRR

Another example of an incidence density design:

• Bronchodilators are used for the treatment of asthma

• There is concern that overuse may be associated withan increased risk of adverse events, including death

• Side effects can include arrhythmias, which may leadto sudden death

• Suissa et al conducted a case-control study using the Saskatchewan health insurance database

• They identified 30 persons prescribed anti-asthma medications who died of cardiovascular events, rather than of asthma; the date of death was termed the index date


• 4080 control days were then sampled randomly from the 574,103 person-months of follow-up for the entire asthmatic group; each such day was also an index date

• Cases and controls were then compared as to use of theophylline and beta-agonists during the 3 months preceding the index date

• These were the main exposures of concern


Questions for discussion:

• Why do you think the researchers chose this study design?

• What would have been the corresponding cohort study?


With respect to the relationship between theophylline use andsudden cardiac death, the authors found the following:

Theophylline in last 3 months

Yes No | TotalCardiac Death Yes 17 13

| 30No 956 3124 | 4080

Note that numbers in table refer to person-days (not to persons)

OR (crude) = ad = 17 x 3124 = 4.3 (2.1 - 8.8)__ ________bc 13 x 956

IRR (crude) = 4.3 (2.1 - 8.8)


The odds of recent theophylline use among personsaged 5-54 years prescribed anti-asthma drugs who died of cardiovascular events were4.3 times those among other persons in the same age range who were also prescribed anti-asthma drugs, but did not die.

“Asthmatics” aged 5-54 who are prescribed theophylline have an estimated 4.3 fold increase in incidence of fatal cardiovascular events, compared with “asthmatics” who are not prescribed theophylline.


As with the cumulative incidence design, an attributable rate fraction can be estimated for exposed persons:

It is: Ie-Io, where Ie = incidence among exposed and ____ Ie Io = incidence among the unexposed

= IRR - 1 = OR - 1______ _____ IRR OR

For the Saskatchewan study, the estimated attributable rate fraction among “asthmatics” who were prescribed theophylline is:

4.3 - 1 = 0.77______ 4.3

Among “asthmatics” aged 5-54 prescribed theophylline, an estimated 77% of fatal cardiovascular events were related to its prescription.


It is also possible to estimate the attributable rate fractionfor the entire population (PAR%)

In a cohort study, this is simply

It - Io, where It = incidence among the total population_____ It Io = incidence among the unexposed

For the corresponding incidence density case-control study, the population attributable rate fraction is

IRR - 1 x proportion of cases who were exposed,____ IRR

estimated as OR - 1 x a_____ ____OR a+b

Similar parameters involving risk can be generated for the cumulative incidence design


For the Saskatchewan study, recall the 2 x 2 table

Theophylline in last 3 months

Yes No | Total

Cardiac death Yes 17 13 | 30No 956 3124 | 4080

OR = 4.3

Pexp |case = 17/30 = 0.57

then PAR fraction = OR -1 x Pexp |case_____ OR

= 4.3 - 1 x 0.57 = 0.44______ 4.3

Among Saskatchewan “asthmatics” aged 5-54, an estimated 44% of cardiovascular deaths relate to theophylline prescriptions.


Attributable rates (rate difference)

The absolute rate difference (i.e., the absolute rate of disease attributable to exposure) is Ie - Io

Data from a standard case-control study alone cannot validly be used to estimate absolute rates of disease.

Even if case ascertainment is complete, the controls represent an unknown and arbitrary fraction of the true person-time at risk.

Hence the rate difference cannot be estimated.


However, incidence rates can be estimated if there is additional knowledge about the amount of person-time at risk

Exposure

(+) (-)

Disease (+) a b

Disease (-) c = f x x Pt d = f x (1- ) x Pt

Then Ie = a = a_____ ___________ x Pt [c/(c+d)] x Pt

Then Io = b = b_________ ___________(1- ) x Pt [d/(c+d)] x Pt

and the rate difference is Ie-Io

where = proportion of person-time which is exposed


Example:

In this nested case-control study, the researchers knew that in the source cohort (Saskatchewan “asthmatics” aged 5-54), there were 47,842 person-years at risk during the study period

The 2x2 table was: Theophylline in last 3 months

Yes No | TotalCardiac death Yes 17 13 | 30

No 956 3124 | 4080


Then the estimated incidence of cardiac death in “asthmatics” prescribed theophylline (Ie) is:

a = 17 = 0.0015 per person-year___________ ________________[c/(c+d)] x Pt 956/4080 x 47,842

And in “asthmatics” who were not prescribed theophylline the estimated incidence (Io) is:

b = 13 = 0.00035 per person-year___________ _________________[d/(c+d)] x Pt 3124/4080 x 47,842

The estimated rate difference is therefore 0.0015-0.00035 = 0.00115 per person-year.

Note that the IRR computed as Ie/Io remains 4.3


Ie and Io may also be estimated if It is known for the source population

Recall that It = (Ie x ) + [Io x (1- )]

But Ie = Io x OR

Then It = Io [(OR x ) + (1- )]

So Io = It = It______________ ________________________ (OR x ) + (1- ) {OR x [c/(c+d)]} + [d/(c+d)]

Then use Ie = Io x OR

Then RD = Ie - Io as usual [= Io (OR-1)]


Example:

The total incidence (It) of cardiovascular death

in the Saskatchewan cohort was 30 deaths/47,842 person-years = 0.00063 per person-year.

Then Io = 0.00063 = 0.00035___________________________[4.3 x (956/4080)] + (3124/4080)

and Ie = 0.00036 x 4.3 = 0.0015

RD = 0.0015 - 0.00035 = 0.00115


Additional points

Corresponding estimates of attributable risks andrisk differences can be made for cumulative incidencecase-control studies, if the corresponding additional datais available

Estimates of absolute risks/incidence rates and risk/rate differences can be made only if thetotal amount of persons/person-time at risk is known, or at least one absolute risk/incidence rate is known (i.e. for the total population, the exposed, or the unexposed)

Nested case-control studies are a special type of studywhere cases and controls are explicitly drawn from a defined larger cohort (as in the Saskatchewan asthma study)



Case-Control Studies: Strengths and Limitations

Advantages of case-control studies:

Efficiency - much less expensive/intensive than cohort studies.

Very useful for outcomes that are rareor occur after a long latency period.

Most outcomes are relatively rare over short-term follow-up.

Permit evaluation of multiple exposures.

Can rapidly “accrue” person-time experience.

Avoid losses to follow-up inherent in cohort studies.

Disadvantages

• Not useful/efficient for very rare exposures (may not be present in either cases or controls).

• Cannot directly compute incidence rates.

• Cannot usually evaluate more than one outcome.

• Temporality may be lost or distorted.

• Potential for considerable bias, i.e. loss of validity.

Bias relates to:

- Measurement of exposure status

- Selection of subjects (usually controls)


With respect to measurement,

exposure ascertainment must be consistent for cases and controls.

There may be potential for misclassification ofexposure in relation to disease status


Example 1

Differential recall of exposures among casesvs controls

e.g. medication use and congenital malformations- particularly if mothers “attuned” to study hypothesis.

If cases more likely to recall exposure, results will be biased toward apositive association between exposure and outcome.

The more objective the source of exposure data, the better.


Example 2

Different sources of information about exposure

e.g. family members asked about alcohol consumption of persons who died of gastric cancer,

vs Direct questioning of control subjects.

If family members tend to underestimate cases’ alcohol consumption, results will be biased against finding a positive association between alcohol and gastric cancer.


Example 3

Exposure status changes as a consequence ofthe outcome

e.g. patients with symptoms of lung cancer stop smoking

If patients with newly diagnosed lung cancer arecompared to controls with respect to currentor recent smoking, results may be biased, i.e.,the association between smoking and lung cancerwill be underestimated.

Data collection must reflect relevant person-timeexperience and temporality of exposure and outcome.


Association may also be missed if the exposure of interest is poorly documented (an example of non-differential misclassification)

Example: mesothelioma It can be caused by brief, intense exposures to asbestos, with a very long latency period (>30 years).

In a case control study, both cases and controls may recall such exposuresvery poorly, thereby leading to an underestimateof the true association.


Control selection in case-control studies

Recall that the validity of case-control studies hinges on the assumption that thesampling fraction for cases (which may be 100%) and that for controls (usually unknown) does not vary by exposure status.

In other words, controls should represent the source population from which the cases arose, with respect to exposure experience.


Example 1

A researcher wishes to test the hypothesis that use of nonsteroidal anti-inflammatory drugs (NSAIDs) is associated with development of gastric cancer.

She plans a case-control study comparing gastric cancer patients (cases) with patients seen at the same hospital for peptic ulcer disease (controls).

- NSAID use is a known risk factor for ulcers.

What will be the effect on her findings:

a) if NSAID use is truly a risk factor for gastric cancer?

b) if NSAID use is truly unassociated with gastric cancer?


Hence, controls should not differ systematically from the population of interest with respect to exposure experience.

Sometimes the bias may be less obvious, i.e. unrelated to explicit criteria for

control selection.


Example 2

A researcher wishes to evaluate the association between cellular phone use and brain tumours using a case-control design.

Cases are recruited from the brain tumour clinic at theRoyal General Hospital, a neurosurgery referral centre.

Controls are recruited from the family medicine clinic at the same hospital. This clinic primarily serves a low-income population from the area adjacent to the hospital.

This control group is less likely than the general populationto own cellular phones.

Result:

The study will be biased toward detecting anassociation between brain tumours and cell phone use.


Controls should be at risk for developing the outcome of interest

- otherwise they do not contribute useful data to the study(inefficient)

- inclusion of individuals not at risk mayalso distort the results if the reason they are not at riskrelates to the exposure under study. This may not be obvious.

Example:

Sleep apnea (exposure) and risk of traffic accidents (outcome)

Cases: Drivers involved in car accidents.

Including non-drivers in the control group would bea waste of time

- it could bias the results ifpersons with severe apnea have chosen not to driveand are over-represented in the control group.


Controls should be persons who,

had they developed the outcome of interest, would have had the same opportunity as the actual cases to be included as such.

Similarly, cases should have

had the same opportunity as actual controls to be included, had they not developed the outcome of interest.

If this is not the case, controls may not properly represent the source population.

e.g., study of brain tumours and cell phone usediscussed above


Types of controls in case-control studies

1. Population Controls

Suitable if cases are a representative sample (or all cases) arising from a well-definedsource population.

Controls are then randomly sampled from the same population.

With the incidence-density design,the probability of being sampled shouldvary with an individual’s person-time at risk.

Often, it is not easy to define the precise source population.


2. Neighbourhood Controls

May match controls to individual cases with respect to neighbourhood of residence.

If cases are from a hospital, their neighbours may or may not be equally likely to be treated at the same hospital should they develop the disease in question.

Example:

A hospital which caters to a particular group

within society.


3. Family members or friends as controls

May share exposure characteristics with casesas opposed to broader source population (e.g. tobacco and alcohol use, dietary intake, use of household products). This can obscure relevant associations.

Depends on information provided by cases;investigator loses control over factors leading to selection.

Cases’ friends may overlap, leading todisproportionate probabilities of selection

of certain individuals as controls.


4. Hospital/clinic based controls

Often used when cases accrued at specifichospital(s)/clinic(s).

Controls are recruited among persons seen at the same hospitals/clinics for other reasons or conditions.

To avoid bias, the basis for control selection cannot be related to the exposure under study.

The incidence of the “control” condition(s) determines the sampling fraction.


Example:

A researcher wishes to examine the relationship between anti-hypertensive medication use and car accidents.

What will happen if controls are recruited in the cardiology clinic?


The best hospital controls are

persons with acute conditions thatconsistently require hospital care but are not related to the exposure of interest.

Example:

In a case control study of smoking as a risk factor for colon cancer, a researcherrecruits controls who undergo appendectomy,prostatectomy, or hysterectomy at the same hospital as the cases.


Derivation of formula - Part 1

For the cohort study, the 2 x2 table is:

exposed unexposed totalCases a b a + b

Person-time Pe Po Pe + Po = Pt

IRR = Ie = a/Pe = aPo___ _____ ____

Io b/Po bPe

= a(Pt - Pe)= a (1 - Pe/Pt)_______ _________ bPe b (Pe/Pt)

= a x (1-)_ ____b

Where = Pe/Pt =the proportion of person-years withexposure among total person-years in the source population

Supplemental Material - Slide 1

Derivation of formula - Part 2

if = proportion of person-years with exposure

then 1- = proportion of person-years without exposure

and It=Ie + Io (1- )

i.e. a weighted average of incidence rates

among exposed and unexposed persons


Then the PAR fraction is:

It - Io = (Ie ) + [(Io (1- )] - Io_____ ____________________ It (Ie ) + [Io (1- )]

= (Ie/Io) + (1- ) (Io/Io) - Io/Io______________________________________

(Ie/Io) + (Io/Io) (1- )

= (IRR) + 1 - - 1________________ (IRR) + 1 -

= (IRR - 1)____________ (IRR - 1) + 1


Derivation - Part 3

= IRR - 1_____________IRR + (1/ ) - 1

= IRR - 1____________IRR + ( 1- )______

= IRR - 1______________IRR + IRR (1- )_________

IRR ()


Substituting equation 1 for IRR, this is

IRR - 1____________________________IRR + IRR (1- ) () (1 - Pexp |case)_______________________

() (Pexp |case) (1- )

= IRR - 1__________________IRR + IRR (1-Pexp |case)_____________

Pexp case

= IRR - 1______________________________IRR (Pexp |case) + IRR - IRR (Pexp |case)______________________________

Pexp case

= IRR - 1 x Pexp |case = OR -1 x Pexp |case______ ____IRR OR


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